id245857953 pdfMachine by Broadgun Software - a great PDF writer! - a great PDF creator! - http://www.pdfmachine.com http://www.broadgun.com
BBiiooTTISSNe e: 097cc4 - h7h435 nnoolVlolouome g8g Issuyye 8
An Indian Journal
FULL PAPER
BTAIJ, 8(8), 2013 [1042-1047] Numerical simulation of javelin best throwing angle based on biomechanical model
Xia Zeng*, Xiongwei Zuo Department of Physical Education, Changsha Medical University, Changsha 410219, (CHINA) E-mail: [email protected]
ABSTRACT KEYWORDS
This paper uses the motion aerodynamics principle to analyze the javelin Biomechanics; flight process, integrates related factors with athletic performance in the Aerodynamics; study of the force condition and movement condition of the human body Throw angle; and the javelin, numerically simulates the different angles of fixed param- Mathematic numerical eters by Mathematic software, obtains the theoretical optimum throwing simulation. °, that is when the shot angle is 40° and the angle of the javelin’s angle 40 ° the throwing distance reaches long axis with the horizontal surface is 31 the greatest. The results are very consistent with the actual situation; this ’s article can make reasonable suggestions for the promotion of this project athletic performance, provides a theoretical basis for the javelin sports technique, and confirms the reasonableness of existing theory and tech- nique. 2013 Trade Science Inc. - INDIA
INTRODUCTION ing sport biomechanics and aerodynamics principle to conduct objective analysis of the javelin throwing move- In the javelin movement, moving trajectory and ment has an actively promoting effect on the develop- moving results of javelin are primarily reflections of a ment of sports technology. set of human movement. Using the biomechanical prin- Javelin throwing process includes: run-up, final force ciples can reasonably prove the maturity of the tech- and javelin releasing flight three phases, where the run- nique and correct errors of technique. When the javelin up phase takes the longest time, and this stage provides releases from the hand it suffers the gravity and air re- the best posture for throwing and at this foundation stage sistance. Due to its shape and mass, it determines that the role of initial kinetic energy is related to achieve- the air resistance of the javelin during movement in the ments; final stage is also used to provide the initial ki- air cannot be ignored, so when we study the moving netic energy for the javelin flight, but its effect is far bet- trajectory of javelin after disposing the aerodynamics ter than the run-up phase, this stage also provides the principle is a good theoretical tool. Only by combining throwing angle of javelin flying, which is critical stage the kinetic characteristics and moving trajectory of the related to athletic performance; During flight javelin re- javelin after disposing can we determine the best shot ceives air resistance and gravity, although the results do angle and speed combination of javelin. Therefore, us- not have a subjective relation, but it provides result refer- BTAIJ, 8(8) 2013 Xia Zeng and Xiongwei Zuo 1043 FULL PAPER ence for the research of validity and rationality of first equivalent to the braking point, as shown in Figure 2. two phases. In this paper, through biomechanics theory and the aerodynamics theory, it conducts a detailed analysis for the three stages of javelin throwing movement, con- firms the reasonableness of the existing technique of this movement combing with the analysis results, and Figure 2 : Schematic of the forearm rotates relatively around provides rationalization proposals for the scientific the elbow joint training. The rotation moment of momentum of the forearm relatively around Point B is as formula (1): SPORTS MECHANICAL ANALYSIS OF LAST â M = I (1) FORCE TECHNIQUE (TAKE THE RIGHT 2 In Formula (1) M represents the torque generated HAND THROWING FOR EXAMPLE) â in the forearm muscle contraction, represents the an- The final stage of javelin throwing technology starts gular acceleration of the forearm around point B. from the right foot, through series of actions delivering According to the definition of angular acceleration by the legs, hips, torso, shoulder, elbow, and hand, and the angular momentum theorem can be obtained as for- finally throw out the javelin. The duration time of the mula (2) below: final stage is about 0.12s-0.15s, which is very short 2 1 M t I 2 ( 2 1 ) (2) from the time interval. But force sequence and speed t Ä change of all aspects of the body are consistent with In Formula (2) t shows the action time of forearm the biomechanics whipping principles. In the braking muscles torque M; by the formula (2) the expression of ù process it has shown a very large instantaneous im- angular velocity 2 can be obtained as formula (3): pulse, makes the javelin have greater instantaneous M t momentum, thus it can have a high initial kinetic energy. 2 1 (3) I 2 In the throwing arm whipping process, when the The formula (3) shows that the angular velocity of hand, forearm and upper arm are in the same line, the ù the forearm is increasing on the basis of in the pro- three links do not exist the relative rotation, but have 1 cess whipping of throwing arm, and the increased value the same angular velocity relative to the shoulder axis, M t as shown in Figure 1. is . I 2 When the rotation angle of forearm around point B is very small, according to the relationship of angular and linear velocity, we have the expressions in formula (4): Figure 1 : The simple schematic when the arm is in straight v r 1 1 1 line v r v r r 2 2 2 1 2 2 (4) In Figure 1 Point A represents the shoulder joint, v v1 v 2 í point B represents the elbow joint, point C represents In Formula (4) represents the linear velocity of í the wrist joint, I1, I2 respectively mean the moment of the point C in wrist relatively to the shoulder joint, ù 1 inertia of upper arm and forearm, 1 means the angular represents the linear velocity of the point B in elbow velocity of the arm rotates straightly around the shoul- í joint relatively to the shoulder joint, 2 represents the der joint. But in the throwing process, forearm and up- linear velocity of the point C in wrist relatively to the per arm has the relative rotation. We suppose the fore- elbow joint, and r , r respectively represents the length arm rotates around the elbow point B, where point B is 1 2 of the upper arm and forearm. BiioTechnollogy An Indian Journal 1044 Numerical simulation of javelin best throwing angle based BTAIJ, 8(8) 2013 FULL PAPER
Substitute the formula (2) and (3) into the formula AERODYNAMIC ANALYSIS (4) formula (5) can be obtained: r M t After disposing in addition to its own gravitational v (r r ) 2 1 1 2 (5) force Javelin also suffers air resistance. Studying the I 2 movement condition of javelin releasing can reflect the According to formula (5), when forearm whips, the relationship between movement characteristics and ath- r M t 2 letic performance when releasing the Javelin, and it is line speed of the wrist increases by I comparing ’s throwing tech- 2 the entry point to study the movement with no whipping. nique problem of non-forces influencing factors, so it is ’s center of gravity In the final force stage, the body necessary to study the movement of the javelin after speed is constantly declining; human kinetic energy is disposing. also reducing. The direction of the braking by the left For any one kind of javelin it has its fixed shape leg landing and the inertia by the throwing arm on the and quality. We can use the polynomial fitting way to javelin in the acceleration process is opposite to the dispose each measurement point, and get the physical ’s speed acceleration direction of the javelin. So the body characteristics parameters of the javelin. This paper is declining, if in the last throwing process of throwing takes the javelin for adult males as the research object, arm, throwing objects, the stronger the force of inertia uses the previous 4 order polynomial function as a model of the throwing matter is, the much thorough that mo- base below. The javelin physics parameters in TABLE mentum transfer of the body on the javelin is. 1 can be obtained. TABLE 1 : Javelin physics parameter table for adult male Parameter name Physical magnitude Total mass of Javelin 811.5g Distance from the gun breech to the centroid 1585mm Distance from centroid to gun head 1055mm × Surface area of Javelin 2.098 105mm2 × The maximum projected area of javelin 6.352 104mm2 × The rotational moment of inertia around its own shaft (the axis perpendicular to the javelin direction) 0.4563 109g*mm2 × The rotational moment of inertia around its own shaft (the axis along the javelin direction) 0.1379 106g*mm2 × The rotational moment of inertia around its own shaft (another axis perpendicular to the javelin direction) 0.4563 109g*mm2 The initial kinetic parameters when releasing javelin include: the shot height of javelin centroid is h , the shot í 0 velocity of centroid is , the angle of javelin centroid 0 è shot velocity with the horizontal surface is , the angle á 0 of javelin with the horizontal plane is , the pitch angu- 0 ù lar velocity when releasing the javelin is 0, the angle of the projection of the javelin long axis in the xoy surface and the projection of the javelin centroid velocity in the ã xoy surface is generally known as the yaw angle, the 0 Figure 3 : The initial state of javelin releasing instant in the releasing moment of the javelin is in the spatial coordi- coordinate system nate system as shown in Figure 3: Javelin suffers gravity vertically downward and re- expression of the friction resistance is in formula (6): sistance generated by air during movement in the air. 1 2 Ff Cf v dS (6) Air resistance is divided into frictional resistance, pres- Sf 2 sure drag and the induced drag. The friction resistance In Formula (6), F means the friction of air on the ñ f is relevant with the air viscosity coefficient, and the javelin, means the air density, C means the viscosity BiioTechnollogy f An Indian Journal BTAIJ, 8(8) 2013 Xia Zeng and Xiongwei Zuo 1045 FULL PAPER coefficient of air, S means the surface area of the jav- INITIAL PARAMETERS AND THROWING í f elin, and ô indicates the relative parallel velocity of jav- DISTANCE NUMERICAL SIMULATION elin centroid to the gas. WHEN JAVELIN RELEASES AWAY FROM The expression of the pressure drag is as the for- THE HAND mula (7): Based on the above force condition of javelin after 1 2 F C v dS p p // (7) disposing, conduct numerical simulation for formula (6) Sp 2 í (7) (8), we can obtain the throwing distance of the jav- In Formula (7) means the relative vertical veloc- elin with different initial parameters. TABLE 2 shows ity of javelin centroid to the gas, and Sp means the pro- the centroid speed of the javelin when shot, the angle of jected area of the javelin. the velocity and the horizontal direction, the angle of Javelin also receives induced drag during the flight. javelin long axis and the horizontal surface and the ini- The air resistance acts on the javelin, decompose the tial yaw angle. In order to explore the problem of shot resistance in a direction relatively parallel to air flow angle, this paper selects the shot speed 26m/s that ath- and relatively perpendicular to air flow. Since in the jav- letes generally can reach in major match, the yaw angle ° elin flight the air joint force that it receives does not is 0 , the air viscosity coefficient is 0.003, pressure drag necessarily act on the javelin centroid, it will produce coefficient is 1.2, the air density is 1.18 * 10-5g/mm3, torsional moment on the javelin. The javelin movement it uses Mathematic software to conduct numerical simu- can be seen as the plane motion in yoz; according to lation for javelin throwing distance, the simulation re- the synergistic effect of the rotation law of rigid body sults are in TABLE 2. and the projectile movement of the objects, the result- TABLE 2 : The combination comparison table of computer ant moment equations in the y axial direction and z axial simulation results direction can be obtained, as shown in formula (8): Shot The angle of Javelin long Throwing 0 angle 0 axis and the horizontal plane distance (m) l 1 ° ° 0 2 2 30 15 62.6 Fpy sin( ) Cp v sin sin f d l1 2 ° ° 30 18 63.4 l ° ° 0 2 2 30 21 64.4 Ffy Cf v cos cos f d l1 2 ° ° 30 24 65.3 l 1 ° ° 0 2 2 30 27 65.8 Fpz sin( ) Cp v sin cos f d l1 2 ° ° 30 30 66.0 l (8) 0 2 2 ° ° Ffz Cf v cos sin f d 30 33 65.9 l1 2 ° ° 30 36 65.9 l 0 1 2 2 ° ° M sin( ) C v sin f d 30 39 65.8 l p 1 2 ° ° 30 42 65.6 ° ° The formula (8) shows that the air resistance will 30 45 65.0 generate rotation torque on the javelin, and the gravity The change trend of throwing distance with 0 when goes the Javelin center of gravity, so the gravity will not ° 0 is 30 is shown in Figure 4: generate rotating torque and the movement of the two forces can be superimposed. The numerical simulation results indicate that when the pitch angular velocity is zero, for the average athlete the range of best shot angle ° ° is between [38 , 44 ], if the pitch angular velocity is not zero, we should appropriately increase the shot angle. When the initial attack angle is 0, the throwing distance of javelin is the farthest; the smaller the air viscosity Figure 4 : The comparison chart of throwing distance and 0 coefficient is, the better throwing distance is. when = 30 0 BiioTechnollogy An Indian Journal 1046 Numerical simulation of javelin best throwing angle based BTAIJ, 8(8) 2013 FULL PAPER
Because there are too much data, it is shown in the form of bar graph also the final result, respectively = ° ° ° ° ° ° 0 32 , 34 , 36 , 38 , 40 , 42 ; the corresponding 0 is shown in Figure 5 - Figure 10.
á Figure 9 : The comparison chart of throwing distance and è ° 0 when 0 = 40
Figure 5 : The comparison chart of throwing distance and º 0 when 0 = 32
á Figure 10 : The comparison chart of throwing distance and è ° 0 when 0 = 42 Figure 4 - Figure 10 shows the following results: è ° and á ° the maximum throwing 1) When 0 = 30 0 = 30 distance is 66.0m; è ° and á ° the maximum throwing 2) When = 32 = 32 á 0 0 Figure 6 : The comparison chart of throwing distance and distance is 67.5m; è ° 0 when = 34 è ° and á ° the maximum throwing 0 3) When 0 = 34 0 = 31 distance is 68.8m; è ° and á ° or 30° the maximum 4) When 0 = 36 0 = 27 throwing distance is 70.5m; è ° and á ° the maximum throwing 5) When 0 = 38 0 = 29 distance is 71.1m; è ° and á ° the maximum throwing 6) When 0 = 40 0 = 31 distance is 71.3m; è ° and á ° the maximum throwing 7) When 0 = 42 0 = 30 á distance is 71.2m; Figure 7 : The comparison chart of throwing distance and è ° 0 è ° when = 36 According to the simulation results, when 0 = 40 0 á ° we have the maximum throwing distance, and 0 = 31 and then with the assumed parameters, this combina- tion is the best throwing angle.
CONCLUSIONS
This paper uses sports biomechanics and aerody- namics to well explain javelin movement, and propose á the best throwing angle and precautions of throwing; Figure 8 : The comparison chart of throwing distance and è ° 0 obtains optimal throwing angle combination by numeri- when = 38 BiioT0 echnollogy An Indian Journal BTAIJ, 8(8) 2013 Xia Zeng and Xiongwei Zuo 1047 FULL PAPER cal simulation. Aerodynamics is the theoretical basis to [3] Haibin Wang, Shuye Yang; An analysis of hurdle study the javelin movement after releasing it, which well performance prediction based on mechanical analy- explains the air resistance of the javelin; in the satisfied sis and gray prediction model. International Journal condition air resistance has a rotational torque role on of Applied Mathematics and Statistics, 39(9), 243- the javelin, so that during the flight it can generate rota- 250 (2013). [4] Hongwei Yang; Evaluation model of physical fit- tion; The numerical simulation results show that when è ° and the angle á ° of the ness of young tennis athletes based on AHP- the shot angle = 40 = 31 0 0 TOPSIS comprehensive evaluation. International javelin with the ground the throwing distance is the great- Journal of Applied Mathematics and Statistics, est, and this combination is the best throwing angle. 39(9), 188-195 (2013). [5] Liao Hong; Study on the optimal release angle of REFERENCES Javelin with air resistance. China Sport Science and Technology, 43(1), (2007). [1] Bing Zhang, Yan Feng; The special quality evalua- [6] Lu Jian-Ming; The function of left side support dur- tion of the triple jump and the differential equation ing the release phase in Javelin throw. China Sport model of long jump mechanics based on gray cor- Science and Technology, 39(4), (2003). relation analysis. International Journal of Applied [7] Wang Qian; Optimal initial conditions for Javelin Mathematics and Statistics, 40(10), 136-143 performance under new rules. Sport Science, 9(2), (2013). 30-35 (1989). [2] Cai Cui; Application of mathematical model for simu- [8] Zhou Li; Current state and analysis of sports bio- lation of 100-meter race. International Journal of mechanics study in China. Journal of Shanghai Applied Mathematics and Statistics, 42(12), 309- Physical Education Institute, 1, 23-26 (1997). 316 (2013).
BiioTechnollogy An Indian Journal